respectively.
As we show below, for problem REF  the two relaxations are equivalent to the original problem in terms of global and local minima.
Using the same arguments, it is also possible to show this equivalence for the cardinality minimization problem.
However, for the cardinality-constrained problem it is known, see [1]}, that only the global minima of the original problem and its relaxation coincide, but the relaxation may have additional local minima.
